Anti-coordination games, such as the Hawk-Dove [1]}, [2]} (also called Snowdrift game [3]}, [4]}) were shown to hold a wide variety of fixation probability function shapes. One of the most striking observations was the pervasiveness of functions with one minimum, a shape which was already noted in [5]} under the fixation of dove strategy. In some orderings, this was the only shape observed when asymptotic values were finite, even for low values of intensity of selection. While it was shown in [6]} that fixation probabilities decrease with population size when the weak selection limit is dominant over the large population limit, our results suggest that if arbitrarily large populations are considered, weak selection does not necessarily erase these non decreasing shapes. Additionally, when approaching the limit where fixation functions change from being asymptotically null to having this shape with a global minimum, all anti-coordination game orderings showed functions with two extremes. Finally, two of these orderings also showed monotonically increasing shapes when \(b\)  was sufficiently large, i.e. when mutants benefited the most from interacting with residents.
